check on (someone or something) means to look into their/it's condition. "I'm going to check on things at the factory. I hope everyone is still working hard." "I'm going to check on my sister and make sure she is doing her homework." check out (someone or something) means to evaluate them/it. "I'm going to check out the competition and see how we compare." "Check out Maria's skirt! It's so cool." "Check out" can also have other meanings, such as "to leave/depart" "I'm checkin' out, friends, see ya later." Or, to take something someone away: "May I check out this book?" (from the library) "I'm here to check my daughter out of school, she's feeling unwell." For a more thorough answer "check out": http://idioms.thefreedictionary.com/check+out and http://idioms.thefreedictionary.com/check+on